Nonlinear fitting of multi-compartmental data using Hooke and Jeeves direct search method

Abstract

Compartmental modelling refers to modelling the transport of substances in a system consisting of multiple compartments, which is characterized by the transfer rates among the relevant compartments. In a generalized compartmental system, recycling of substances among the compartments is allowed. Compartmental modelling is a generic technique which is needed in many branches of applied physics. The most challenging task is to determine the transfer rates. The present work described the use of the Hooke and Jeeves (HJ) derivative free direct search method in determining the transfer rates to construct a multi-compartmental model with recycling among the compartments. The use of a direct search method ensures the applicability of the model to functions which are not continuous or differentiable. The present model was successfully validated using previously reported experimental data for distribution of trace elements in four compartments in an animal.

Fitting a three-dimensional sphere by the least squares method

“…For nonlinear functions, if the previous method is used: the fitted nonlinear equation 𝑦 = 𝑓(𝑥 1 , 𝑥 2 , ⋯ , 𝑥 𝑖 ; 𝑎 0 , 𝑎 1 , ⋯ , 𝑎 𝑛 ) is directly substituted into its deviation equation and then the partial derivatives are taken to make it zero, the unknown parameter 𝑎 0 , 𝑎 1 , ⋯ , 𝑎 𝑛 derived by this method is very complicated and difficult to express [5]. Therefore, the general method is to expand the nonlinear function in accordance with the Taylor series in turn, which should be ignored the highest number of terms, and then the Taylor series after the expansion of the linear representation of the method of least squares and then use the least squares method in the linear fitting method to find out all the unknown parameters, the final approximation to meet the requirements of its accuracy after a number of times.…”